Computing the Cosmos

One of the biggest computer simulations ever run is illuminating the deepest mysteries of the universe

By Alexander Hellemans and Madhusree Mukerjee

Posted 1 Aug 2004 | 4:00 GMT

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If cosmologists were to make a movie of the universe's entire history, the show would start, of course, withthe scorching blast of the Big Bang. The universe--absolutelyevery bit of mass we can detect or even infer today--wouldexpand at unfathomable speeds, going from smaller thana proton to larger than a galaxy in the blink of aneye. As the expansion continued, the universe wouldcool down, and by the time the opening credits of themovie finished scrolling, a superhot soup of elementaryparticles would fill the whole cosmos, ready to cookthe first protons and neutrons.But what would happennext?

The fact is, cosmologists are still working out the restof the plot--what exactly took place during the morethan 13 billion years since that primeval blast. [Forthis article, in keeping with the current trend in internationalscientific publishing, IEEE Spectrum uses thewords "billion" to mean 109 and "trillion" tomean 1012.] A particular piece of the storythat has kept researchers scratching their heads is howgalaxies formed and evolved. How did that amorphous particlesoup transform itself into billions and billions of galaxiesof breathtakingly different shapes and sizes? Why didthese galaxies gather together in clusters, and clustersof clusters, embedded along unimaginably enormous structuresof matter shaped like bubbles, filaments, and sheets?

To answer these and other fundamental questions in cosmology,an international group of scientists from Canada, Germany,the United Kingdom, and the United States has been workingon an ambitious project whose goal is to simulate ona supercomputer the evolution of the entire universe,from just after the Big Bang until the present.

The group, dubbed the Virgo Consortium--a name borrowedfrom the galaxy cluster closest to our own--is creatingthe largest and most detailed computer model of the universeever made. While other groups have simulated chunks ofthe cosmos, the Virgo simulation is going for the wholething. The cosmologists' best theories about the universe'smatter distribution and galaxy formation will becomeequations, numbers, variables, and other parameters insimulations running on one of Germany's most powerfulsupercomputers, an IBM Unix cluster at the Max PlanckSociety's Computing Center in Garching, near Munich.

Late this year, the group plans to begin storing all of itsoutput data in public repositories available to researchers around the world [see "Downloading the Sky" in this issue]. This accessibility, according to Simon D.M. White, a research director at the Max PlanckInstitute for Astrophysics who leads the German participation inthe Virgo Consortium, will allow researchers to compareeach simulated universe to its ultimate benchmark: theuniverse itself, as observed with ground and space telescopes.

If the simulation produces a bizarre universe that doesn'tresemble ours, the assumptions that underpin the simulationare probably flawed or in need of adjustment. On theother hand, if the virtual cosmos is like the one wesee, researchers will know they are on the right track.In this way, they hope to see some of the deepest mysteriesof the cosmos solved on their computer screens.

By peering into great distances with powerful telescopes, astronomers have discovered a startlingpattern of, literally, cosmic proportions: galaxiesgather into clusters of varying sizes that don't floatin isolation in the universe but rather are linkedto one another by long tendrils of matter. What's more,these agglomerations of clusters are collected ontoincredibly huge bubbles, filaments, and sheetlike structures,millions of light-years in size.

These structures, the grandest that are known, form a three-dimensionalcosmic web that fills the universe. If you could shrinkthe cosmos until a galaxy cluster were the size of agrain of sand, a chunk plucked out of this universalweb would resemble a piece of a kitchen sponge; the airpockets in the sponge would represent the huge cosmicvoids that contain almost no matter [see illustration, " ]."

To find out how and when this giant clumpy web formed, theVirgo group is simulating how matter dispersed in spaceover almost the entire course of the universe's existence.

To begin creating their model of the universe, the researchers faced two basic questions: at whatmoment, precisely, should they start the simulation?And what are the universe's conditions at that verymoment? Fortunately, cosmologists believe they havethese answers.

According to the inflationary universe theory put forward in the1980s by Alan Guth, of the Massachusetts Institute ofTechnology, and Andrei Linde, of Stanford University,the universe swelled at an extraordinarily rapid rateduring a tiny fraction of a second immediately afterthe Big Bang. This exponentially fast expansion amplifiedminute, quantum-scale fluctuations that existed in theprimordial energy field that filled the very early universe.These fluctuations caused matter to clump, and later,gravity created denser and denser aggregates.

The result is that these aggregates, which began as unimaginablysmall energy fluctuations in that primeval universe muchsmaller than a proton, ultimately evolved into the giantstructures that compose the universe's spongelike webof matter. Even more surprising, most of the mass inthis web of matter is not the ordinary stuff we knowthat makes up galaxies, stars, planets, and people.

After many experiments and calculations throughout the pastdecade, most cosmologists now agree on the astoundingfact that some 85 percent of the matter in the universeconsists of a mysterious substance known as dark matterthat cannot be seen directly. They infer its presenceby tracking the motions of stars and galaxies: starsare attracted to the centers of galaxies, and galaxiesto the centers of galaxy clusters, by gravitational forcesthat are far greater than visible matter alone can possiblyaccount for. Something else must be out there.

This shadowy substance is made up not of the familiar quarks,electrons, and their derivatives--atoms and molecules--butof some particle that has so far eluded experimenters.Candidates include axions, photinos, neutralinos--allyet to be discovered--among other particles predictedby theorists. The upshot is that, because dark matteris not visible, what astronomers have observed are thecontours of the universe's great web, revealed by thelight of the stars and galaxy clusters that formed ontothe web's nodes, the junctions at which large amountsof matter accumulate. It's kind of like inferring theshape of a Christmas tree in a pitch-dark room from thepositions of the lights strung on it. These stars, galaxies,and other objects that we can see were born from denseaggregates of normal matter embedded in the dark matterof the web.

One of the major cosmological features that the Virgo teamrelies on to formulate its simulations is something calledthe cosmic microwave background, a feeble radiation remnantof the Big Bang that astronomers have now studied ingreat detail. This radiation, a key piece of evidencesupporting the inflation theory, was emitted 380 000years after the Big Bang when protons combined with freeelectrons to form neutral hydrogen atoms.

If the cosmic particle soup were absolutely smooth, withevenly distributed hydrogen atoms, this radiation wouldalso be smooth all over the place--always the samewherever you look. But as cosmologists pointed theirdetectors to different parts of the sky, they found smallvariations in the cosmic microwave background. Thesevariations were recently minutely detailed by NASA'sWilkinson Microwave Anisotropy Probe, whose first scientificresults were made public early last year. In a triumphof modern cosmology, the measured variations correspondprecisely with the predictions of inflation theory.

The cosmic microwave background, therefore, gives cosmologistsa fairly good picture of the distribution of matter whenthe universe, with an estimated current age of 13.7 billionyears, was still in its infancy, only 380 000 years old.That's the starting point the Virgo group has chosenfor its simulations. The main one, the first of a series,dubbed the Millennium Run, was completed this past June.When data is fully processed within the next few months,the Millennium Run will reveal with unprecedented detailhow the cosmos's broad distribution of matter came tobe. "It will be the mother of all simulations," saysCarlos S. Frenk, a cosmology professor at the Universityof Durham, United Kingdom, who leads the British participationin the Virgo Consortium.

On the charming campus of the Max Planck Institute,it's not difficult to find its supercomputer center:just follow the sound of the loudest air conditioners.They're chilling the computer cluster--two longrows of refrigerator-size black boxes occupying a shinywhite room--used by the Virgo astrophysicists,as well as by other associated research groups [see photo, " "].

The machine, a cluster of powerful IBM Unix computers, hasa total of 812 processors and 2 terabytes of memory,for a peak performance of 4.2 teraflops, or trillionsof calculations per second. It took 31st place late lastyear in the Top500 list, a ranking of the world's mostpowerful computers by Jack Dongarra, a professor of computerscience at the University of Tennessee in Knoxville,and other supercomputer experts.

But as it turns out, even the most powerful machine on Earthcouldn't possibly replicate exactly the matter distributionconditions of the 380 000-year-old universe the Virgogroup chose as the simulation's starting point. The numberof particles is simply too large, and no computer nowor in the foreseeable future could simulate the interactionof so many elements.

So the fundamental challenge for the Virgo team is to approximatethat reality in a way that is both feasible to computeand fine-grained enough to yield useful insights. TheVirgo astrophysicists have tackled it by coming up witha representation of that epoch's distribution of matterusing 10 billion mass points, many more than any othersimulation has ever attempted to use.

These dimensionless points have no real physical meaning; they are just simulation elements, a way ofmodeling the universe's matter content. Each pointis made up of normal and dark matter in proportionto the best current estimates, having a mass a billiontimes that of our sun, or 2000 trillion trillion trillion(239) kilograms. (The 10 billion particlestogether account for only 0.003 percent of the observableuniverse's total mass, but since the universe is homogeneouson the largest scales, the model is more than enoughto be representative of the full extent of the cosmos.)

Cosmologists will let these massive points interact exclusively throughgravity, which prevails over all the other forces atthe scale of the simulation. The points will be evenlydistributed in space many millions of light-years apartfrom one another, except for small variations in theirpositions that mimic the density inhomogeneities of theearly universe. These slight displacements resultingfrom the inflationary expansion ensure that some pairsof particles find themselves closer to each other andtherefore move even closer, until they join up. Ultimately,this flow of matter will end up weaving the universe'sweb, with its dark-matter filaments, clumps of galaxies,and gargantuan voids.

But if all pieces of matter in the universe are attractingone another gravitationally, will the universe eventuallycollapse upon itself in a reverse Big Bang? It's a questionthat has nagged at researchers since Sir Isaac Newton'stime.

The answer emerges from a discovery a few years ago thatjolted scientists' concept of the cosmos. For decadescosmologists have been studying the universe's expansionby looking at the light emitted by the most distant observablegalaxies. The distance this light has to travel is constantlyincreasing as the universe expands and galaxies, theEarth, and everything else get farther and farther apart.As a result, the light's wavelength is "stretched" andthus shifted toward the red part of the spectrum (owingto a phenomenon called the Doppler effect).

Measuring this redshift, astrophysicists can calculate the speedof galaxies' motion and can thereby infer the Hubbleconstant. Named after astronomer Edwin Hubble, who in1929 found that the universe is expanding, this numberdescribes how fast any two points in the fabric of space-timeare currently moving apart. In 1998 observations of distantsupernovae demonstrated that the expansion of the universeis not slowing down but accelerating--news that stunnedcosmologists.

After a few thousand time steps, the simulated universe should come to resemble the one we live in

As early as 1917, Albert Einstein had conceived a solution to a similar puzzle. He realized that if the attraction of matter prevailed in the universe, it would ultimately pull the universe inward into collapse. So he postulated a hypothetical quantity, the cosmological constant, to provide repulsion and hold the universe steady. Although Einstein later rejected his cosmological constant, calling it his greatest blunder, theorists have now resurrected a similar entity--dark energy--to explain the ever-faster expansion of the universe.

This dark energy, whose mere existence still baffles many physicists, repels everything, including itself, and therefore cannot clump. Instead, the dark energy spreads into a sort of haze that fills the universe and pushes against its outer limits. The true nature of dark energy remains, if anything, even more elusive than that of dark matter.

Cosmologists resort to a two-dimensional analogy to explain the outcome of this expansion-clumping balance: think of ants living on a balloon that is constantly being blown up. Much as they would all like to get together, the best they could manage would be little ant congregations scattered around the balloon. In other words, the pull of gravity still causes matter to clump, despite the repulsion of dark energy, but it clumps into clusters separated by great voids in which the density of matter is extremely low.

In the Virgo simulation, the virtual universe, contained in a cube, expands a thousand times, until each of its sides grows to more than two billion light-years [see illustration, " "].The present rate of the expansion is dictated by the Hubble constant, whose value the scientists get from the latest observations. In the end, the simulation produces a virtual cube with enough room for the largest cosmic structures in the universe and enough detail to catch the cosmic web's formation in the act. That's the hope, anyway.

On a blissfully sunny holiday , the Max Planck astrophysics institute is mostly empty, except for a few self-conscious scientists slinking in and out of offices, clearly embarrassed to be caught working on such a beautiful day. One of them is astrophysicist Volker Springel, a researcher who designed much of the algorithm that puts the virtual universe's mass in motion. The software he and his colleagues developed calculates the gravitational interactions among the simulation's 10 billion mass points and keeps track of the points' displacements in space. It repeats these calculations over and over, for thousands of simulation time steps. But what seems to be merely a repetitive calculation task turns out to be a computational nightmare.

Unlike other forces, such as the strong force that binds quarks into protons or neutrons and that doesn't extend beyond an atomic nucleus, gravity never dies off completely, no matter how far apart an assortment of bodies are from one another. The simulation, therefore, has to calculate the gravitational pull between each pair of mass points. That is, it has to choose one of the 10 billion points and calculate its gravitational interaction with each of the other 9999999999 points, even those at the farthest corners of the universe. Next, the simulation picks another point and does the same thing again, with this process repeated for all points. In the end, the number of gravitational interactions to be calculated reaches 100 million trillion (1 followed by 20 zeros), and that's just for one time step of the simulation. If it simply chugged through all of the thousands of time steps of the Millennium Run, the Virgo group's supercomputer would have to run continuously for about 60000 years.

This computational barrier is known as the n2 bottleneck. In general terms, to know how an assembly of n points interacts gravitationally, you have to compute a total of n x (n - 1) interactions, or approximately n2 when n is large. To overcome this barrier, the Virgo group had to use some tricks.

First, the researchers divided the simulated cube into several billion smaller volumes. During the gravitational calculations, points within one of these volumes are lumped together--their masses are summed. So instead of calculating, say, a thousand gravitational interactions between a given particle and a thousand others, the simulation uses an algorithm to perform a single calculation if those thousand points happen to fall within the same volume. For points that are far apart, this approximation doesn't introduce notable errors, while it does speed up the calculations significantly.

This approach, however, does not work well at short distances, because it blurs the effects of relatively small clumps of matter. In other words, the simulation loses resolution, and researchers can miss significant events. So Springel developed new software with what is called a tree algorithm to simplify and speed up the calculations for this realm of short-distance interactions. Think of all 10 billion points as the leaves of a tree. Eight of these leaves attach to a stem, eight stems attach to a branch, and so on, until all the points are connected to the trunk. To evaluate the force on a given point, the program climbs up the tree from the root, adding the contributions from branches and stems found along the way until it encounters individual leaves.

This trick reduces the number of required calculations from an incomputable n2 to a much more manageabl en log 10 n, says Springel, who combined the two algorithms in a single program. With such calculation shortcuts, he says, the Millennium Run took 26 days to run on the Max Planck Institute supercomputer. It yielded 20 TB of data in 64 snapshots of the virtual universe, from birth to its present state.

Total darkness reigned in the universe in a cosmic dark age that began a few million years after the Big Bang and lasted for hundreds of millions of years. The universe was expanding and cooling, and matter was gathering in the gigantic strands and nodes of the cosmic web. No stars existed to illuminate the cosmos.

Then the birth of stars and galaxies heralded a new phase, in which a whole new menagerie of heavy atoms came into existence and new celestial objects multiplied in all corners of the cosmos. This led to planets, and eventually even to people, who would marvel at it all.

Over many decades, astrophysicists have built up a picture of how these events unfolded. Gravity compresses dark matter and normal matter, the latter in the form of hydrogen and a little helium, into a dense mass at a node in the cosmic web. This compressed cloud of gas and dark matter is not static but swarming with motion. Since dark matter has no electromagnetic interactions, it cannot radiate and therefore always retains its kinetic energy. But normal matter--hydrogen and a few other particles--radiates some of this energy and yields to the pull of gravity. It settles into the center of the clump, moving in ever-tighter circles, like water swirling down a bathtub drain.

Angular momentum arranges the gas into a ragged spiral. When it is dense enough, stars start to form: hydrogen nuclei begin fusing, creating helium and heavier elements and giving off light. The brilliantly studded spiral disk of such an infant galaxy, now typically having a radius of 10 000 light-years, is embedded within a far larger halo of dark matter. Our Milky Way, for example, has a spiral disk with a 50 000-light-year radius surrounded by a spherical halo of dark matter with a radius that is 10 times as great.

Gravity continues to draw nearby cosmic aggregates of matter ever closer, so that the newly born star disks frequently smash into one another. Some astrophysicists believe that most large galaxies, with their many different shapes, are formed as a result of collisions. Although most of the stars in the colliding galaxies pass by one another, gravity pulls them out of their neat disks into chaotic orbits, creating an irregular galaxy.

Eventually, the galaxies coalesce completely, their stars' orbits being entangled so thoroughly that they constitute a smooth elliptical galaxy. Any remaining hydrogen is reenergized in the collision, so that, in time, it radiates again, settles toward the center, and then forms a new disk around the elliptical core.

In this way, collisions can lead to a large spiral galaxy with a central bulge. The Milky Way has such a central bulge containing very ancient stars, some 10 billion years old; it almost certainly resulted from one or more collisions roughly eight billion years ago. The beautiful spiral arms, home to our sun, are a relatively recent acquisition, most of the stars within them being only a few billion years old.

That's precisely the kind of story the Virgo astrophysicists hope to see unfolding in their simulation. The recently completed Millennium Run gave them the universe's broad distribution of matter as dictated by gravity. In upcoming simulations, other forces will come into play. Onto the web of matter the scientists will graft the electromagnetic aspects of normal matter, which by radiating photons allows gas to cool down and condense into spiral disks that originate stars. At the same time, hydrodynamic pressure, which ultimately derives from the fact that two atoms cannot overlap each other because of repulsion between their electrons, redistributes matter along the cosmic web's strands and nodes.

If all goes well, the cosmic web will then light up, becoming populated by galaxies--spiral, elliptical, irregular--as well as nebulae, stars, and star clusters. Stars and supernovae, the spectacular explosions by which stars die, will feed energy and heavier elements, such as oxygen and carbon, back into the surrounding gas. These effects, in combination, should lead to galaxies that look a lot like the ones we actually see. And as the galaxies move, they will collide and reconstitute. Little by little, the cosmic web will acquire galaxies of various shapes and sizes, each within a neighborhood that corresponds with its history.

After a few thousand time steps, the simulated universe should come to resemble the one we live in, with its staggering diversity in the forms and density accumulated matter takes. "The idea is to make a small number of physically motivated assumptions and let those rip, and see how close you get to the real world," says Virgo member John A. Peacock, a cosmology professor at the University of Edinburgh, in the United Kingdom.

The Virgo scientists hope their simulation will be detailed enough to be statistically representative of the real universe. That means that while they won't be able to point to a galaxy and say, "This is the Milky Way," they will be able to search their virtual universe and find a section of it that looks like the Milky Way. And then they will be able to follow this section back to study its history and learn about how the real Milky Way came to be.

In the end, the simulations will help cosmologists refine their theories, which, like all theories, attempt to portray reality accurately. Discrepancies will point to deficiencies in theorists' understanding of star and galaxy formation, or possibly even in observers' interpretations of their data. The exchanges will let scientists continually refine both the virtual universe and the observational strategies used with real telescopes.

For milennia , human beings have been contemplating the heavens, trying to decipher the celestial mysteries. From Ptolemy and Aristotle in ancient Greece to Einstein and Hubble, stargazers have come up with ever more elaborate models of the universe. But as it turns out, the current generation of cosmologists is tackling the kinds of problems they may not be able to solve by jotting down equations on paper or peering through telescopes.

They have made remarkable progress with their cosmological theories, but many fundamental questions remain. When were the first stars really born? Why do galaxies have the shapes and sizes they have? How much dark matter, exactly, is out there? What is in the huge labyrinthine voids entangled in the cosmic web? For some of these questions, supercomputers may provide the long-sought answers.